Structural Engineering and Mechanics

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Global sensitivity analysis improvement of rotor-bearing system based on the Genetic Based Latine Hypercube Sampling (GBLHS) method

  • Fatehi, Mohammad Reza (Mechanical Engineering Department, Shahid Chamran University of Ahvaz) ;
  • Ghanbarzadeh, Afshin (Mechanical Engineering Department, Shahid Chamran University of Ahvaz) ;
  • Moradi, Shapour (Mechanical Engineering Department, Shahid Chamran University of Ahvaz) ;
  • Hajnayeb, Ali (Mechanical Engineering Department, Shahid Chamran University of Ahvaz)
  • Received : 2017.09.17
  • Accepted : 2018.10.23
  • Published : 2018.12.10
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Abstract

Sobol method is applied as a powerful variance decomposition technique in the field of global sensitivity analysis (GSA). The paper is devoted to increase convergence speed of the extracted Sobol indices using a new proposed sampling technique called genetic based Latine hypercube sampling (GBLHS). This technique is indeed an improved version of restricted Latine hypercube sampling (LHS) and the optimization algorithm is inspired from genetic algorithm in a new approach. The new approach is based on the optimization of minimax value of LHS arrays using manipulation of array indices as chromosomes in genetic algorithm. The improved Sobol method is implemented to perform factor prioritization and fixing of an uncertain comprehensive high speed rotor-bearing system. The finite element method is employed for rotor-bearing modeling by considering Eshleman-Eubanks assumption and interaction of axial force on the rotor whirling behavior. The performance of the GBLHS technique are compared with the Monte Carlo Simulation (MCS), LHS and Optimized LHS (Minimax. criteria). Comparison of the GBLHS with other techniques demonstrates its capability for increasing convergence speed of the sensitivity indices and improving computational time of the GSA.

Keywords

References

  1. Benaroya, H. and Rehak, M. (1988), "Finite element methods in probabilistic structural analysis: A selective review", Appl. Mech. Rev., 41(5), 201-213. https://doi.org/10.1115/1.3151892
  2. Campolongo, F., Carboni, J. and Saltelli, A, (2007), "An effective screening design for sensitivity analysis of large models", Environ. Modell. Softw., 22, 1509-1518. https://doi.org/10.1016/j.envsoft.2006.10.004
  3. Crombecq, K. and Dhaene, T. (2006), "Generating sequential space-silling designs using genetic algorithms and Monte Carlo methods", Comput. Indust. Eng., 50, 503-527. https://doi.org/10.1016/j.cie.2005.07.007
  4. De Lozzo, M. and Marrel, A. (2015), "Estimation of the derivative-based global sensitivity measures using a Gaussian process metamodel", SIAM/ASA J. Uncertain. Quantific., 4, 708-738.
  5. Didier, J., Faverjon, B. and Sinou, J.J. (2012), "Analyzing the dynamic response of a rotor system under uncertain parameters by polynomial chaos expansion", J. Vibr. Contr., 18, 587-607. https://doi.org/10.1177/1077546311408470
  6. Didier, J., Sinou, J.J. and Faverjon, B. (2012), "Study of the nonlinear dynamic response of a rotor system with faults and uncertainties", J. Sound Vibr., 331, 671-703. https://doi.org/10.1016/j.jsv.2011.09.001
  7. Duchereau, J. and Soize, C. (2003), "Transient dynamic induced by shocks in stochastic structures", Appl. Stat. Probab. Civil ICASP, 9, 1-6.
  8. Faber, M.H. (2005), "On the treatment of uncertainties and probabilities in engineering decision analysis", J. Offshore Mech. Arct. Eng., 127, 243-248. https://doi.org/10.1115/1.1951776
  9. Gan, C., Wang, Y., Yang, S. and Cao, Y. (2014), "Nonparametric modeling and vibration analysis of uncertain Jeffcott rotor with disc offset", Int. J. Mech. Sci., 76, 126-134.
  10. Gobbato, M., Conte, J., Koshmatka, J. and Farra, C. (2012), "A reliability-based framework of fatigue damage prognosis of composite aircraft structures", Probab. Eng. Mech., 29(1), 176-188. https://doi.org/10.1016/j.probengmech.2011.11.004
  11. Grosso, A., Jamali, A.R.M.J.U. and Locatelli, M. (2009), "Finding maximin Latin hypercube designs by iterated local search heuristics", Eurz. Oper. Res. J., 197(2), 541-547. https://doi.org/10.1016/j.ejor.2008.07.028
  12. Guo, X., Zhao, X., Zhang, W., Yan, J. and Sun, G. (2015), "Multi-scale robust design and optimization considering load uncertainties", Comput. Meth. Appl. Mech. Eng., 283, 994-1009. https://doi.org/10.1016/j.cma.2014.10.014
  13. Guo, Y. and Parker, R.G. (2012), "Stiffness matrix calculation of rolling element bearings using a finite element/contact mechanics model", Mech. Mach. Theor., 51, 32-45. https://doi.org/10.1016/j.mechmachtheory.2011.12.006
  14. Hickernell, F.J. (1998), "A generalized discrepancy and quadrature error bound", Math. Comput., 67, 299-322. https://doi.org/10.1090/S0025-5718-98-00894-1
  15. Iooss, B. and Lemaitre, P. (2015), A Review on Global Sensitivity Analysis Methods, Meloni, C. and Dellino, G. Uncertainty Management in Simulation-Optimization of Complex Systems: Algorithms and Applications, Springer.
  16. Jafari, P. and Jahani, E. (2016), "Reliability sensitivities with fuzzy random uncertainties using genetic algorithm", Struct. Eng. Mech., 60(3), 413-431. https://doi.org/10.12989/SEM.2016.60.3.413
  17. Jin, R., Chen, W. and Sudjianto, A. (2005), "An efficient algorithm for constructing optimal design of computer experiments", J. Stat. Plan. Infer., 51, 268-287.
  18. Johnson, M.E., Moore, L.M. and Ylvisaker, D. (1990), "Minimax and Maximin distance design", J. Stat. Plan. Infer., 24, 131-148.
  19. Jones, A.B. and Poplawski, J. (1966), "A computer study of design parameters on rolling element bearing performance", Proceedings of the Bearings Conference at Dartmouth University.
  20. Jourdan, A. (2012), "Global sensitivity analysis using complex linear models", 22, 823-831. https://doi.org/10.1007/s11222-011-9239-y
  21. Krishnaiah, P.R. (1981), Analysis of Variance, Elsevier, New York, U.S.A.
  22. Kundu, A., DiazDelaO, F.A., Adhikari, S. and Friswell, M.I. (2014), "A hybrid spectral and metamodeling approach for the stochastic finite element analysis of structural dynamic systems", Comput. Meth. Appl. Mech. Eng., 270, 201-219. https://doi.org/10.1016/j.cma.2013.11.013
  23. Liao, H. (2014), "Global resonance optimization analysis of nonlinear mechanical systems: Application to the uncertainty quantification problems in rotor dynamics", Commun. Nonlin. Sci. Numer. Simulat., 19(9), 3323-3345. https://doi.org/10.1016/j.cnsns.2014.02.026
  24. Lim, T.C. and Singh, R. (1990), "Vibration transmission through rolling element bearings, part I: Bearing stiffness formulation", J. Sound Vibr., 139, 179-199. https://doi.org/10.1016/0022-460X(90)90882-Z
  25. Liu, Y., Jeong, H.K. and Collette, M. (2016), "Efficient optimization of reliability-constrained structural design problems including interval uncertainty", Comput. Struct., 277, 1-11.
  26. McKay, M.D., Conover, W.J. and Beckman, R.J. (1979), "A comparison of three methods for selecting values of input variables in the analysis of output from a computer code", Technometr., 21(2), 239-245. https://doi.org/10.1080/00401706.1979.10489755
  27. Michael, D., Shields, N. and Zhang, J. (2016), "The generalization of Latin hypercube sampling", Reliab. Eng. Syst. Safety, 148, 96-108. https://doi.org/10.1016/j.ress.2015.12.002
  28. Minh, D.D., Gao, W. and Song, C. (2016), "Stochastic finite element analysis of structures in the presence of multiple imprecise random field parameters", Comput. Meth. Appl. Mech. Eng., 300, 657-688. https://doi.org/10.1016/j.cma.2015.11.032
  29. Mirzaee, A., Shayanfar, M. and Abbasnia, R. (2015), "A novel sensitivity method to structural damage estimation in bridges with moving mass", Struct. Eng. Mech., 54(6), 1217-1244. https://doi.org/10.12989/SEM.2015.54.6.1217
  30. Mitchell, T.J. (1974), "Computer construction of d-optimal first-order designs", Technometr., 16, 211-220.
  31. Morris, M.D. (1991), "Factorial sampling plans for preliminary computational experiments", Technometr., 33, 161-174. https://doi.org/10.1080/00401706.1991.10484804
  32. Morris, M.D. and Mitchell, T.J. (1995), "Exploratory designs for computer experiments", J. Stat. Plan. Infer., 43, 381-402. https://doi.org/10.1016/0378-3758(94)00035-T
  33. Muscolino, G., Santoro, R. and Sofi, A. (2016), "Reliability assessment of structural systems with interval uncertainties under spectrum-compatible seismic excitation", Probab. Eng. Mech., 44, 138-149. https://doi.org/10.1016/j.probengmech.2015.11.005
  34. Olsson, A.M.J. and Sandberg, G.E. (2002), "On Latin hypercube sampling for stochastic finite element analysis", J. Eng. Mech., 128(1), 121-125. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:1(121)
  35. Olsson, G., Sandberg, O. and Dahlblom. (2003), "On Latin hypercube sampling for structural reliability analysis structural safety", 25, 47-68. https://doi.org/10.1016/S0167-4730(02)00039-5
  36. Paolino, D.S., Chiandussi, G. and Belingardi, G. (2013), "Uncertainty in fatigue loading: Consequences on statistical evaluation of reliability in service", Probab. Eng. Mech., 33, 38-46. https://doi.org/10.1016/j.probengmech.2013.02.001
  37. Park, J. (1994), "Optimal Latin-hypercube designs for computer experiments", J. Stat. Plan. Infer., 39, 95-111. https://doi.org/10.1016/0378-3758(94)90115-5
  38. Pate-Cornell, M.E. (1996), "Uncertainties in risk analysis: Six levels of treatment", Reliab. Eng. Syst. Safety, 54, 95-111. https://doi.org/10.1016/S0951-8320(96)00067-1
  39. Petryna, Y.S. and Kratzig, W.B. (2005), "Compliance-based structural damage measure and its sensitivity to uncertainties", Comput. Struct., 83, 1113-1133. https://doi.org/10.1016/j.compstruc.2004.11.020
  40. Rafal, S., Piotr, T. and Michal, K. (2007), "Efficient sampling techniques for stochastic simulation of structural systems", Comput. Assist. Mech. Eng. Sci., 14, 127-140.
  41. Rennen, G., Husslage, B., Van Dam, E.R. and Hertog, D. (2010), "Nested maximin Latin hypercube designs", Struct. Multidisc. Optim., 41, 371-395. https://doi.org/10.1007/s00158-009-0432-y
  42. Ritto, T.G., Lopez, R.H., Sampaio, R. and Souza, J.E. (2011), "Robust optimization of a flexible rotor-bearing system using the Campbell diagram", Eng. Optim., 43, 77-96. https://doi.org/10.1080/03052151003759125
  43. Saltelli, A., Chan, K. and Scott, E.M. (2000a), Sensitivity Analysis, Wiley Series in Probability and Statistics, Wiley.
  44. Saltelli, A., Ratto, M., Andres, T., Cariboni, J., Gatelli, D., Tarantola, S., Campolongo, F. and Saisana, M. (2008), Global Sensitivity Analysis, The Primer, John Wiley & Sons, U.S.A.
  45. Saltelli, A., Tarantola, S. and Campolongo, F. (2000b), "Sensitivity analysis as an ingredient of modeling", Stat. Sci., 15, 379-390.
  46. Saltelli, A., Tarantola, S., Campolongo, F. and Ratto, M. (2004), Sensitivity Analysis in Practice, A guide to Assesing Scientific Models, John Wiley & Sons, U.S.A.
  47. Sepahvand, K. and Marburg, S. (2013), "On construction of uncertain material parameters using generalized polynomial chaos expansion from experimental data", Proc. IUTAMG., 4-17.
  48. Sinou, J.J. and Jacqueliin, E. (2015), "Influence of polynomial chaos expansion order on an uncertain asymmetric rotor system response", Mech. Syst. Sign. Proc., 50, 718-731.
  49. Sobol, I.M. (1993), "Sensitivity analysis for non-linear mathematical models", Math. Model. Comput. Exper., 1, 407-414.
  50. Sobol, I.M. (1993), "Sensitivity analysis for non-linear mathematical models", Math. Model. Comput. Exper., 1, 407-410.
  51. Soize, C. (2000), "A nonparametric model of random uncertainties for reduced matrix models in structural dynamics", Probab. Eng. Mech., 15, 277-294. https://doi.org/10.1016/S0266-8920(99)00028-4
  52. Stocki, R., Szolc, T., Tauzowski, P. and Knabel, J. (2012), "Robust design optimization of the vibrating rotor-shaft system subject to selected dynamic constraints", Mech. Syst. Sign. Proc., 29, 34-44. https://doi.org/10.1016/j.ymssp.2011.07.023
  53. Szolc, T., Tauzowski, P., Stocki, R. and Knabl, J. (2009), "Damage Identification in vibrating rotor-shaft systems by efficient sampling approach", Mech. Syst. Sign. Proc., 23, 1615-1633. https://doi.org/10.1016/j.ymssp.2008.12.007
  54. Tondel, K., Vik, J.O., Martens, H., Indahl, U.G., Smith, N. and Omholt, S.W. (2013), "Hierarchical multivariate regression-based sensitivity analysis reveals complex parameter interaction patterns in dynamic models", Chemometr. Intellig. Laborat. Syst., 120, 25-41. https://doi.org/10.1016/j.chemolab.2012.10.006
  55. Vorechovsky, M. and Novak, D. (2009), "Correlation control in small-sample Monte Carlo type simulations I: A simulated annealing approach", Prob. Eng. Mech., 24, 452-462. https://doi.org/10.1016/j.probengmech.2009.01.004
  56. Wei, J.J. and Lv, Z.R. (2015), "Structural damage detection including the temperature difference based on response sensitivity analysis", Struct. Eng. Mech., 53(2), 249-260. https://doi.org/10.12989/SEM.2015.53.2.249
  57. Ye, K.Q., Li, W. and Sudjianto, A. (2000), "Algorithmic construction of optimal symmetric Latin hypercube designs", J. Stat. Plann. Infer., 90, 145-159. https://doi.org/10.1016/S0378-3758(00)00105-1
  58. Zhao, J. and Wang, C. (2014), "Robust topology optimization under loading uncertainty based on linear elastic theory and orthogonal diagonalization of symmetric matrices", Comput. Meth. Appl. Mech. Eng., 273, 204-218. https://doi.org/10.1016/j.cma.2014.01.018

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